Although the movie is credited as having been "suggested by the book by A. Conan Doyle," in fact the plot is very different from that of the novel itself, which first introduced the character of Sherlock Holmes to the general public. Even the characters other than Sherlock Holmes and Dr. Watson are not the original ones that appeared in the story.
The film uses the "ten little Black boys" nursery rhyme gimmick--a new verse of this rhyme is sent to each victim just before he is killed--also used by Agatha Christie in her book, variously called "Ten Little Indians" and "And Then There Were None." However, Christie didn't publish her novel until 1939, six years after this film was made.
The reason "A Study in Scarlet" used only the title of Arthur Conan Doyle's first Sherlock Holmes story and not Doyle's actual plot is that the Conan Doyle estate quoted the producers a price for the rights to the title and a considerably higher price to use the original story. So the producers paid the lower price and hired "B" director Robert Florey to write a new story, though he and dialogue/continuity writer Reginald Owen peppered their script with allusions to other Holmes stories by Conan Doyle.
The failure of the original copyright holder to renew the film's copyright resulted in it falling into public domain, meaning that virtually anyone could duplicate and sell a VHS/DVD copy of the film. Therefore, many of the versions of this film available on the market are either severely (and usually badly) edited and/or of extremely poor quality, having been duped from second- or third-generation (or more) copies of the film.